This was a missing role since the beginning of Office 365 and Exchange Online to allow the delegation of the administration of the quarantine.
Before you had to create your very own Exchange Role with the correct permissions – Mail Recipient, Message Tracking, Transport Hygiene and View-Only Configuration (which was not easy to find as there was no documentation).
Well good news, a new Quarantine Administrator role is becoming available through the Security and Compliance portal (https://protection.office.com/), providing an out-of-the-box Role Based Access to the quarantine management.
To define the membership, logon to your Security and Compliance portal (https://protection.office.com/) and reach out the Permissions blade
Then look up the roles list to find the Quarantine Administrator one
NOTE this role is NOT (yet?) available through the Office 365 main administration portal (https://admin.microsoft.com/)